Simplify the following expression: $ y = \dfrac{-3}{5} + \dfrac{4a + 9}{-3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3}{-3}$ $ \dfrac{-3}{5} \times \dfrac{-3}{-3} = \dfrac{9}{-15} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{4a + 9}{-3} \times \dfrac{5}{5} = \dfrac{20a + 45}{-15} $ Therefore $ y = \dfrac{9}{-15} + \dfrac{20a + 45}{-15} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{9 + 20a + 45}{-15} $ $y = \dfrac{20a + 54}{-15}$ Simplify the expression by dividing the numerator and denominator by -1: $y = \dfrac{-20a - 54}{15}$